<!DOCTYPE html>
<html lang="zh-cn">
  <head>
  <meta charset="utf-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="author" content="Zhou Wei <zromyk@163.com>">
  <title>数学-真题</title>
  <link rel="shortcut icon" href="/favicon.ico">
  <link rel="stylesheet" href="/style/html/pure.css">
  <link rel="stylesheet" href="/style/html/main.css">
  <link rel="stylesheet" href="https://cdn.staticfile.org/font-awesome/4.7.0/css/font-awesome.css">
  <!-- <link rel="stylesheet" href="https://apps.bdimg.com/libs/highlight.js/9.1.0/styles/default.min.css"> -->
<link rel="stylesheet" href="/style/article/highlight/default.min.css">
<link rel="stylesheet" href="/style/article/pell-1.0.6/dist/pell.css">

</head>
<body>
  <div id="menu-background"></div>
  <div id="menu">
    <div class="pure-menu pure-menu-horizontal">
  <ul class="pure-menu-list block-middle">
    <li class="pure-menu-item">
  <a class="pure-menu-heading" href="/index.html">ZROMYK</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link" href="/index.html">主页</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link" href="/public/archive/index.html">归档</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link" href="/public/download/index.html">下载</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link" href="/public/feedback/index.html">反馈</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link" href="/public/about/index.html">关于我</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link" href="https://github.com/zromyk"><i class="fa fa-github" style="font-size:32px"></i></a>
</li>

  </ul>
</div>

  </div>
  <div id="layout">
    <div class="content">
      <div id="nav">
    <div id="navigation" class="navigation">
  <ul class="pure-menu-list">
    <li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20072-ycfrac1xln1ex">【2007.2】曲线 <script type="math/tex">y=\cfrac{1}{x}+\ln(1+e^x)</script> 渐近线的条数为【】</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20074-fx-x0">【2007.4】设函数 <script type="math/tex">f(x)</script> 在 <script type="math/tex">x=0</script> 处连续，下列命题 <strong>错误</strong> 的是【】</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20084-fx-inftyinfty-x_n">【2008.4】设函数 <script type="math/tex">f(x)</script> 在 <script type="math/tex">(-\infty,+\infty)</script> 内单调有界，<script type="math/tex">\{x_n\}</script> 为数列，下列命题正确的是【】</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20085-a-n-e-n-a3o">【2008.5】设 <script type="math/tex">A</script> 为 <script type="math/tex">n</script> 阶非零矩阵，<script type="math/tex">E</script> 为 <script type="math/tex">n</script> 阶单位矩阵，若 <script type="math/tex">A^3=O</script>，则【】</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20087-xy-x-fx-zmaxxy">【2008.7】设随机变量 <script type="math/tex">X,Y</script> 独立同分布，且 <script type="math/tex">X</script> 的分布函数为 <script type="math/tex">F(x)</script>，则 <script type="math/tex">Z=\max\{X,Y\}</script> 的分布函数为【】</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20094-a_nb_n-lim_ntoinftya_n0">【2009.4】设有两个数列 <script type="math/tex">\{a_n\}\{b_n\}</script>，若 <script type="math/tex">\lim_{n\to\infty}a_n=0</script>，则【】</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20097-x-fx03phix07phicfracx-12-phix-ex">【2009.7】设随机变量 <script type="math/tex">X</script> 的分布函数为 <script type="math/tex">F(x)=0.3\Phi(x)+0.7\Phi(\cfrac{x-1}{2})</script>，其中 <script type="math/tex">\Phi(x)</script> 为标准正态分布的分布函数，则 <script type="math/tex">E(x)</script> =【】</a>
</li>
<li class="pure-menu-item">
  <a class="pure-menu-link nav5" onclick="animateByNav()" href="#20098-x-y-x-n01y-py0py1cfrac12-f_zz-zxy-f_zz">【2009.8】设随机变量 <script type="math/tex">X</script> 与 <script type="math/tex">Y</script> 相互独立，且 <script type="math/tex">X</script> 服从标准正态分布 <script type="math/tex">N(0,1)</script>，<script type="math/tex">Y</script> 的概率分布为 <script type="math/tex">P\{Y=0\}=P\{Y=1\}=\cfrac{1}{2}</script>，记 <script type="math/tex">F_z(z)</script> 为随机变量 <script type="math/tex">Z=XY</script> 的分布函数，则函数 <script type="math/tex">F_z(z)</script> 的间断点个数为【】</a>
</li>

  </ul>
</div>

</div>
<div id="content-articles">
  <h1 id="数学-真题" class="content-subhead">数学-真题</h1>
  <p>
    <span>1970-01-01</span>
    <span><span class="post-category post-category-math">Math</span></span>
    <button id="button-markdownEditor" class="pure-button" onclick="markdownEditor()">启用编辑</button>
    <button id="button-save" class="pure-button" onclick="save()">保存</button>
  </p>
  <div id="content-articles-markdownEditor" style="display: none;">
    <h1>编辑 power by pell</h1>
    <div id="editor" class="pell"></div>
    <div style="margin-top:20px;">
        <h3>Text output:</h3>
        <div id="text-output"></div>
    </div>
    <div style="margin-top:20px;">
        <h3>HTML output:</h3>
        <pre id="html-output"></pre>
    </div>
  </div>
  <div id="content-articles-markdown">
    <h5 id="20072-ycfrac1xln1ex">【2007.2】曲线 <script type="math/tex">y=\cfrac{1}{x}+\ln(1+e^x)</script> 渐近线的条数为【】</h5>
<p><img class="pure-img" alt="截屏2021-11-09 22.53.05" src="https://zromyk.gitee.io/myblog-figurebed/post/数学-真题.assets/截屏2021-11-09 22.53.05.png" /></p>
<h5 id="20074-fx-x0">【2007.4】设函数 <script type="math/tex">f(x)</script> 在 <script type="math/tex">x=0</script> 处连续，下列命题 <strong>错误</strong> 的是【】</h5>
<p>A. 若 <script type="math/tex">\lim_{x\to0}\cfrac{f(x)}{x}</script> 存在，则 <script type="math/tex">f(0)=0</script>
</p>
<p>B. 若 <script type="math/tex">\lim_{x\to0}\cfrac{f(x)+f(-x)}{x}</script> 存在，则 <script type="math/tex">f(0)=0</script>
</p>
<p>C. 若 <script type="math/tex">\lim_{x\to0}\cfrac{f(x)}{x}</script> 存在，则 <script type="math/tex">f'(0)=0</script> 存在</p>
<p>D. 若 <script type="math/tex">\lim_{x\to0}\cfrac{f(x)-f(-x)}{x}</script> 存在，则 <script type="math/tex">f'(0)=0</script> 存在</p>
<p><img class="pure-img" alt="截屏2021-11-09 22.53.42" src="https://zromyk.gitee.io/myblog-figurebed/post/数学-真题.assets/截屏2021-11-09 22.53.42.png" /></p>
<h5 id="20071601-cfrac12-underline">【2007.16】在区间（0，1）中随机地取两个数，则这两个数之差的绝对值小于 <script type="math/tex">\cfrac{1}{2}</script> 的概率为 <script type="math/tex">\underline{\ \ \ \ \ \ \ \ \ \ \ \ }</script>
</h5>
<p><img class="pure-img" alt="截屏2021-11-09 22.59.13" src="https://zromyk.gitee.io/myblog-figurebed/post/数学-真题.assets/截屏2021-11-09 22.59.13.png" /></p>
<hr />
<h5 id="20084-fx-inftyinfty-x_n">【2008.4】设函数 <script type="math/tex">f(x)</script> 在 <script type="math/tex">(-\infty,+\infty)</script> 内单调有界，<script type="math/tex">\{x_n\}</script> 为数列，下列命题正确的是【】</h5>
<p>A. 若 <script type="math/tex">\{x_n\}</script> 收敛，则 <script type="math/tex">\{f(x_n)\}</script> 收敛</p>
<p>B. 若 <script type="math/tex">\{x_n\}</script> 单调，则 <script type="math/tex">\{f(x_n)\}</script> 收敛</p>
<p>C. 若 <script type="math/tex">\{f(x_n)\}</script> 收敛，则 <script type="math/tex">\{x_n\}</script> 收敛</p>
<p>D. 若 <script type="math/tex">\{f(x_n)\}</script> 单调，则 <script type="math/tex">\{x_n\}</script> 收敛</p>
<h5 id="20085-a-n-e-n-a3o">【2008.5】设 <script type="math/tex">A</script> 为 <script type="math/tex">n</script> 阶非零矩阵，<script type="math/tex">E</script> 为 <script type="math/tex">n</script> 阶单位矩阵，若 <script type="math/tex">A^3=O</script>，则【】</h5>
<p>A. <script type="math/tex">E-A</script> 不可逆，<script type="math/tex">E+A</script> 不可逆</p>
<p>B. <script type="math/tex">E-A</script> 不可逆，<script type="math/tex">E+A</script> 可逆</p>
<p>C. <script type="math/tex">E-A</script> 可逆，<script type="math/tex">E+A</script> 可逆</p>
<p>D. <script type="math/tex">E-A</script> 可逆，<script type="math/tex">E+A</script> 不可逆</p>
<h5 id="20087-xy-x-fx-zmaxxy">【2008.7】设随机变量 <script type="math/tex">X,Y</script> 独立同分布，且 <script type="math/tex">X</script> 的分布函数为 <script type="math/tex">F(x)</script>，则 <script type="math/tex">Z=\max\{X,Y\}</script> 的分布函数为【】</h5>
<p>A. <script type="math/tex">F^2(x)</script>
</p>
<p>B. <script type="math/tex">F(x)F(y)</script>
</p>
<p>C. <script type="math/tex">1-[1-F(x)]^2</script>
</p>
<p>D. <script type="math/tex">[1-F(x)][1-F(y)]</script>
</p>
<h5 id="20089-xyy0-y11-yunderline">【2008.9】微分方程 <script type="math/tex">xy'+y=0</script> 满足条件 <script type="math/tex">y(1)=1</script> 的解是 <script type="math/tex">y=\underline{\ \ \ \ \ \ \ \ \ \ \ \ }</script>
</h5>
<h5 id="200810-sinxylny-xx-01-underline">【2008.10】曲线 <script type="math/tex">sin(xy)+\ln(y-x)=x</script> 在点（0，1）处的切线方程是 <script type="math/tex">\underline{\ \ \ \ \ \ \ \ \ \ \ \ }</script>
</h5>
<h5 id="200812-sigma-zsqrt4-x2-y2-iint_sigma-xydydzxdzdxx2dxdyunderline">【2008.12】设曲面 <script type="math/tex">\Sigma</script> 是 <script type="math/tex">z=\sqrt{4-x^2-y^2}</script> 的上侧，则 <script type="math/tex">\iint_\Sigma xydydz+xdzdx+x^2dxdy=\underline{\ \ \ \ \ \ \ \ \ \ \ \ }</script>
</h5>
<hr />
<h5 id="20094-a_nb_n-lim_ntoinftya_n0">【2009.4】设有两个数列 <script type="math/tex">\{a_n\}\{b_n\}</script>，若 <script type="math/tex">\lim_{n\to\infty}a_n=0</script>，则【】</h5>
<p>A. 当 <script type="math/tex">\sum_{n=1}^\infty b_n</script> 收敛时，<script type="math/tex">\sum_{n=1}^\infty a_nb_n</script> 收敛</p>
<p>B. 当 <script type="math/tex">\sum_{n=1}^\infty b_n</script> 发散时，<script type="math/tex">\sum_{n=1}^\infty a_nb_n</script> 发散</p>
<p>C. 当 <script type="math/tex">\sum_{n=1}^\infty |b_n|</script> 收敛时，<script type="math/tex">\sum_{n=1}^\infty a_n^2b_n^2</script> 收敛</p>
<p>D. 当 <script type="math/tex">\sum_{n=1}^\infty |b_n|</script> 发散时，<script type="math/tex">\sum_{n=1}^\infty a_n^2b_n^2</script> 发散</p>
<h5 id="20097-x-fx03phix07phicfracx-12-phix-ex">【2009.7】设随机变量 <script type="math/tex">X</script> 的分布函数为 <script type="math/tex">F(x)=0.3\Phi(x)+0.7\Phi(\cfrac{x-1}{2})</script>，其中 <script type="math/tex">\Phi(x)</script> 为标准正态分布的分布函数，则 <script type="math/tex">E(x)</script> =【】</h5>
<p>A. 0        B. 0.3        C. 0.7        D. 1</p>
<h5 id="20098-x-y-x-n01y-py0py1cfrac12-f_zz-zxy-f_zz">【2009.8】设随机变量 <script type="math/tex">X</script> 与 <script type="math/tex">Y</script> 相互独立，且 <script type="math/tex">X</script> 服从标准正态分布 <script type="math/tex">N(0,1)</script>，<script type="math/tex">Y</script> 的概率分布为 <script type="math/tex">P\{Y=0\}=P\{Y=1\}=\cfrac{1}{2}</script>，记 <script type="math/tex">F_z(z)</script> 为随机变量 <script type="math/tex">Z=XY</script> 的分布函数，则函数 <script type="math/tex">F_z(z)</script> 的间断点个数为【】</h5>
<p>A. 0        B. 1        C. 2        D. 3</p>
<h5 id="200910-yaby0-yc_1c_2xex-yaybyx-y02y00-yunderline">【2009.10】若二阶常系数微分方程 <script type="math/tex">y''+a'+by=0</script> 的通解为 <script type="math/tex">y=(C_1+C_2x)e^x</script>，则非齐次方程 <script type="math/tex">y''+ay'+by=x</script> 满足条件 <script type="math/tex">y(0)=2,y'(0)=0</script> 的解为 <script type="math/tex">y=\underline{\ \ \ \ \ \ \ \ \ \ \ \ }</script>
</h5>
<h5 id="200912-omegaxyzx2y2z2le1-iiint_omega-z2dxdydzunderline">【2009.12】设 <script type="math/tex">\Omega=\{(x,y,z)|x^2+y^2+z^2\le1\}</script>，则 <script type="math/tex">\iiint_\Omega z^2dxdydz=\underline{\ \ \ \ \ \ \ \ \ \ \ \ }</script>
</h5>
  </div>
</div>
 
    </div>
  </div>
  <div id="footer-background">
    <div id="footer">
      <div class="legal pure-g">
  <div class="pure-u-1 u-sm-1-2">
    <p class="legal-license"><a href="https://beian.miit.gov.cn/#/Integrated/index">浙ICP备2020038748号</a></p>
  </div>
  <div class="pure-u-1 u-sm-1-2">
    <p class="legal-links"><a href="https://github.com/zromyk">GitHub</a></p>
    <p class="legal-copyright">Copyright © 2021 Wei Zhou. 保留所有权利。</p>
  </div>
</div>
    </div>
  </div>
  <!-- <script src="https://cdn.bootcss.com/jquery/3.2.1/jquery.min.js"></script> -->
  <script src="/style/html/jquery.min.js"></script>
  <script src='/style/article/latex/latest.js?config=TeX-MML-AM_CHTML'></script>
<!-- <script src="https://cdn.geogebra.org/apps/deployggb.js"></script> -->
<script src="/style/article/deployggb.js"></script>
<!-- <script src="https://apps.bdimg.com/libs/highlight.js/9.1.0/highlight.min.js"></script> -->
<script type="text/javascript">
  // 脚本：navigation 随鼠标移动自动变换宽度
  var element = document.getElementById("navigation"); // 获取要操作的元素
  var elementWidth = parseInt(getComputedStyle(element).width);
  var elementLeft = 0;
  var elementRight = 0;
  element.addEventListener('mouseenter', function (event) { // 添加鼠标按下事件的监听器
    elementLeft = element.getBoundingClientRect().left - 10;
    elementRight = element.getBoundingClientRect().left + elementWidth * 3;
    window.addEventListener('mousemove', resize); // 添加全局的鼠标移动事件的监听器
  });

  function resize(event) {
    var minWidth = elementWidth;
    var maxWidth = elementWidth * 2.5;
    // console.log(elementLeft, event.clientX, elementRight, event.clientX - elementLeft + elementWidth / 2);
    if (elementLeft <= event.clientX && event.clientX <= elementRight) {
      var width = event.clientX - elementLeft + elementWidth / 2;
      width = Math.min(width, maxWidth);
      width = Math.max(width, minWidth);
      element.style.width = width + 'px'; // 设置新的宽度样式属性
    }
    else {
      element.style.width = elementWidth + 'px'; // 设置新的宽度样式属性
      stopResize();
    }
  }

  function stopResize() {
    element.style.width = elementWidth + 'px'; // 设置新的宽度样式属性
    // console.log("stopResize", elementLeft, event.clientX, elementRight, event.clientX - elementLeft + elementWidth / 2);
    window.removeEventListener('mousemove', resize); // 移除鼠标移动事件的监听器
  }
</script>
<script src="/style/article/highlight/highlight.min.js"></script>
<script type="text/javascript">
  // 脚本：code语法高亮
  hljs.initHighlightingOnLoad();
</script>
<script>
  function animateByNav() {
    $("html").animate({
        scrollTop: ($(event.target.hash).offset().top - 52)
    }, 300);
  };
</script>
<script src="/style/article/pell-1.0.6/dist/pell.js"></script>
<script>
  // 脚本：自由编辑页面
  var editor = window.pell.init({
    element: document.getElementById('editor'),
    defaultParagraphSeparator: 'p',
    onChange: function(html) {
        document.getElementById('text-output').innerHTML = html
        document.getElementById('html-output').textContent = html
    }
  });

  function markdownEditor() {
    var articles = document.getElementById('content-articles-markdown');
    if (articles.getAttribute("contenteditable") == "true") {
        articles.setAttribute("contenteditable", "false");
        document.getElementById("content-articles-markdownEditor").style.display = "none"; //隐藏
        document.getElementById("button-markdownEditor").innerHTML = "启用编辑";
    } else {
        articles.setAttribute("contenteditable", "true");
        document.getElementById("content-articles-markdownEditor").style.display = ""; //显示
        document.getElementById("button-markdownEditor").innerHTML = "关闭编辑";
    }
  };

  function save() {
      window.alert("保存成功");
  };
</script>

</body>
</html>
